A309851 Primes formed by concatenating n and 2n-1.

11, 23, 47, 59, 1019, 1223, 1427, 1733, 2039, 2141, 2243, 2447, 2549, 2753, 2957, 3467, 3671, 4079, 4283, 4691, 4793, 5099, 52103, 55109, 61121, 65129, 70139, 75149, 77153, 82163, 86171, 95189, 102203, 104207, 112223, 119237, 124247, 130259, 132263, 137273, 145289, 146291, 147293, 149297, 150299, 160319

Offset: 1

Author

A.H.M. Smeets, Aug 20 2019

Keywords

• nonn
• base

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A052089 (n and n-1), A030458 (n and n+1), A309808 (n and 2n+1).

Programs

Magma

[a:m in [1..170]|IsPrime(a) where a is 10^(#Intseq(2*m-1))*m+2*m-1]; // Marius A. Burtea, Oct 09 2019

Mathematica

f[n_] := FromDigits @ (Join @@ IntegerDigits[{n, 2n-1}]); Select[f /@ Range[160], PrimeQ]  (* Amiram Eldar, Sep 24 2019 *)

Python

from sympy import isprime
A309851_list = [m for m in (int(str(n)+str(2*n-1)) for n in range(1,10**5)) if isprime(m)] # Chai Wah Wu, Oct 23 2019